Ugly scenes in the crowd delayed kickoff at the Parc Olympique Lyonnais by 45 minutes.
Lyon were charged with insufficient organisation and a breach of safety regulations as their fans blocked stairways, set off fireworks and invaded the pitch after the home team's second goal completed a comeback 2-1 win.
Visiting Besiktas were charged with their fans setting off fireworks, throwing objects and crowd disturbances.
Clashes between rival fans started hours before the kickoff after around 15,000 Besiktas supporters arrived in Lyon, marching through the city centre and lighting flares.
Lyon said their fans sought refuge on the pitch after they were pelted with objects and flares from the upper tiers of the stadium.
The bans will cover the next European club competition for which each team qualifies.
"The CEDB (Control, Ethics and Disciplinary Body) has considered that the supporters of both clubs were responsible for the crowd disturbances at the match," UEFA said in a statement.
The teams meet in the second leg in Turkey on Thursday.
($1 = 0.9337 euros)
(Reporting by Toby Davis, editing by Ed Osmond)
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